DENSITY OF A LIQUID (Lab 2)
Note: Text in black is from the lab manual. Text in other colors are additional comments and instructions put into this help page.

This lab teaches skills in measuring the density of a liquid, and the liquids used are solutions of salt (NaCl). This lab also stresses techniques to get the most accurate measurement of density for a liquid.

If you ever own a salt water aquarium, you can check the salt level (salinity) by doing a density measurement. You can even use the techniques learned here to do that.

Determining density is a straightforward measurement and quite useful for many situations.

aquarium

Introduction

In this experiment you will determine the density of an unknown liquid. You will measure the mass of a known volume delivered from a pipet and use the expression:

M
V
D
=

where D = density, M = mass and V = volume to calculate the density of the unknown liquid.

Mass can be any unit of mass (grams, pounds, tons, etc.) and volume can be any unit of volume (liters, gallons, milliliters, cubic centimeters, etc.). However, the typical units when measuring density is grams for mass and milliliters for volume.

By dividing by grams by the milliliters, you find the mass per one milliliter (g/mL).

Procedure

Part A
Obtain a 10.00mL pipet (preferably a class A pipet), a pipet bulb, a 125 mL Erlenmeyer flask (should be in your drawer), and an unknown from the stockroom. (Note: pipet can also be spelled pipette). The unknowns are solutions of salt dissolved in water.

The CHM151 density unknown will probably be sitting in the lab rather than being in the stockroom. Record the number (or letter) of your unknown before you begin work!!

Here's the collection of items that you need for Part A:

The 125 Erlenmeyer flask (middle).

A 100mL beaker (left).

A 200 mL waste beaker (upper left).

The 10mL pipette (second from bottom).

Instead of a pipet bulb, you will be using a pipette pump (green cylinder on bottom).

Pipette, flask, beaker, pipettor

Again, instead of getting the unknowns from the stockroom, the unknowns are likely to bewhere reagents for the lab are usually stored. You will be using either unknown A, B, or C.

Next to these bottles is a sign under the protective plastic that says:

DO NOT CONTAMINATE REAGENT BOTTLES

THIS MEANS: NOTHING GETS POURED BACK.

(Roll cursor over the image on the right to see this sign.) You will be taking about 40 mL out of one of these bottles. You will also have some of this solution left over. Do not pour your leftover solution back into any of these bottles. By doing so you could contaminate these solutions.

The 10mL volumetric pipettes are stored on the same table as the Unknown solutions. They are stored upside down to facilitate draining.

Volumetric pipettes have only one mark. That's the line that marks the printed volume. Some pipettes have several marks and are called "graduated pipettes". They aren't as accurate as the volumetric types.

If you look close at the printed label, you will get more information. See below image for details.

10 mL pipettes
close up look at pipette label

The lab manual mentions the pipette bulb and shows a diagram of how to use it. The pipette bulb is one way of drawing up liquid and releasing it. It is the red spherical object in the image on the right.

Another device is for doing that is the pipette pump (green and white). It has a thumb-wheel that lets you draw up liquid. As the wheel in turned, a plunger goes up. A partial vacuum will cause air pressure to push liquid up into the pipette. The pipette pump is a little easier to use than the pipette bulb, so that will be the type you will use in this lab.

Roll cursor over the image on the right to see the bin of pipette pumps you will be using in the lab.

Part A Procedure (continued)

Pour about 30 to 50 mL of your unknown into a clean 100 mL beaker.

You will first use this unknown liquid to rinse your flask and pipette. Then you will measure out 10mL for measuring density.

pouring unknown into 100mL beaker
Pour about 5 milliliters of the unknown into the flask. Grab the flask with a paper towel to prevent fingerprints. Swirl the liquid around to rinse the sides of any previous liquid or solids. Then discard the rinsing into the 200 mL waste beaker. Repeat this three times to ensure a clean flask.
Rinse flask sequence

Now you want to weigh the flask. Grab the flask with a paper towel to keep your fingerprints off of the flask. That's because fingerprints add weight. Also, wipe off any liquid that might be on the outside of the flask.

Instead of using a paper towel, you could wear gloves instead.

The lab manual says to use tongs to carry the flask. This could be done, but tongs have a tendency to slip. Since the flask is not hot, you can carry it using piece of a paper towel. If it were hot, then tongs would be used.

It is OK that there is some residue of unknown liquid in the flask because ou will be subtracting the weight of the flask and residual liquid.

 

Grab flask with paper towel
Carry the flask over to one of the Mettler balances in the lab. Before placing the beaker onto the balance pan, "tare" the balance by pressing the TARE button on the right. A different model Mettler balance uses the symbol "O/T" (mean zero or tare). (roll cursor over image on the right to see the other Mettler balance). The word "tare" is from Arabic "tarah" meaning to throw away. In essence by pressing the tare button, we are telling the balance to throw away any weight on the balance so we get a zero starting point.

Again, you are holding the flask with a paper towel to prevent fingerprints.

Set the flask down gently on the balance pan. Close the lid and check the weight.

 

set flask on balance

Record the gram reading in your lab manual. This is the weight of an "empty" flask. Again, the residual liquid is counted as part of the empty (or beginning) weight of the flask. When you add 10 mL of liquid and reweigh the flask, you will be subtracting the starting flask mass. That will give you just the mass of the 10 mL of added liquid.

Weigh the stoppered flask on the Mettler Balance to 0.001 g. Record the weight on line 2 of the data sheet. (Having a rubber stopper on the flask is optional. If you use it now, you have to use it after adding the 10 mL of unknown solution to consistent). This flask weighed 64.215 g. Yours will be different.

 
Trail 1
Trail 2
Trail 3
1. Mass of container and unknown
g
g
g
2. Mass of container
64.215 g
g
g
3. Mass of unknown
g
g
g
4. Volume of unknown used
10.00 mL
10.00 mL
10.00 mL
5. Calculated density
g/mL
g/mL
g/mL
6. Average density of unknown  
Flask being weighed

You will now use the 10 mL pipette to add 10 mL of the unknown solution. Before you do that, you need to rinse out the pipette. See below for details.

Before you can rinse out the 10 mL pipette, you need to attach it to the pipette pump.

Unscrew the white collar a few revolutions. This widens the internal compression ring so the pipette can go in without too much force.

unscrew pipette pump end
Important: Grab near the upper end of the pipette. This will ensure that you don't bend the pipette and break it. Breaking it in your hand almost guarantees getting cut. Grab upper end of pipette
Important: As you insert the top end of the 10mL pipette into the collar of of the pipette pump, turn the pump to reduce the pressure needed to insert the pipette. Remember you are working with glass and you don't want it to break in your hand. Remember, do not bend the pipette. It needs to go straight in while you twist the pipette pump to make it go in easier. Turn pipette pump
After the pipette is inserted, twist the white collar and the green body in opposite directions to tighten it. This should create an airtight seal. You will know if there's an air leak when you draw liquid into the pipette. The liquid level will drop on its own if there's an air leak Tighten Collar
Push the plunger all the way down. This will allow the maximum volume of liquid to be drawn up into the pipette. Push plunger

To rinse out the 10 mL pipette, set the tip into the beaker with the unknown liquid.

Turn the thumbwheel to draw up liquid (roll cursor over image to see use of thumbwheel).

Turn thumbwheel slowly to draw liquid up towards the top of the pipette (about 2 inches below the white collar of the pipette pump).

You will now discard this liquid because it is just being used to rinse out the pipette. See the the below image on how to cause the liquid to drain out.

 

 

On the side of the pipette pump is the white fast-release lever. Press this when you want to let the liquid flow out of the pipette.

The liquid you drew up first is only for rinsing out the pipette. Push the fast-release lever to let the liquid drain into the waste beaker.

Release liquid by pushing button on pump

After discarding the liquid, draw up more liquid to fill the pipette about half way. Tilt the pipette at an angle and turn it to let the liquid rinse off the sides. Don't tilt it so much that it runs into the pipette pump. Drain the the liquid out into the waste beaker. You can press the plunger down to get the liquid out faster.

Draw up the liquid a third time to fill the pipette about one third full. Tilt the pipette at an angle to do a final rinse of the sides. Discard this rinsing into the waste beaker.

Now you will draw up the liquid a fourth time. Bring the level about and inch or two above the 10 mL mark.

Raise the pipette so that its tip is above the surface of the unknown liquid. That's because when the tip is below the surface, water pressure pushes liquid upwards giving a false high reading.

Push the release lever to bring the meniscus (bottom of curved surface) of the liquid to be level with the 10 mL mark. Your eyes need to be level with the mark. See below image for a better view.

set pipette into beaker
After you get the meniscus level with the 10 mL mark, you will move the pipette over to the Erlenmeyer flask that you just weighed. (This photo was taken from a high angle so the eyes look higher than they really were. They were level with the mensicus.) Eye level view

Press the white fast-release lever to allow the 10 mL to drain into the flask.

When the liquid stops draining, there will often be a drop of liquid clinging to the tip of the pipette. Simply touch it to the inside of the flask and it will come off.

 

Flask and pipette
Notice that there should be a little liquid left in the pipette. Remember, this particular pipette is the "TD" type meaning it will deliver 10 mL by draining out. If the pipette stated that it was a "TC" type, then that means "To Contain" in which case you blow out the last bit of liquid because it "contains" 10 mL. However, this TD pipette delivers 10 mL and its accuracy requires this amount of liquid remaining in the pipette. liquid still in pipette
Use a piece of a paper towel to grab the flask with the 10 mL of solution and carry it to the Mettler balance. Again, instead of a paper towel, you could use gloves. If you are skilled with tongs, then that is OK. Unfortunately, many students drop the flask when using tongs. Fill flask grabbed with paper towel

Like always, press the TARE or the 0/T button on the balance to zero out the balance. Then carefully place the flask on the balance.

Record the weight of the flask with th 10 mL unknown liquid in line 1 of the data sheet (Here is 74.228) . You can now subtract the container's mass from the mass of flask and unknown liquid just to get the mass of the unknown liquid. In our example, the liquid weighed 10.013 g. We find density by dividing the mass by the volume. So 10.013g / 10.00 mL equals 1.0013 g/mL, which is slightly more dense than water.

 
Trail 1
Trail 2
Trail 3
1. Mass of container and unknown
74.228 g
g
g
2. Mass of container
64.215 g
g
g
3. Mass of unknown
10.013 g
g
g
4. Volume of unknown used
10.00 mL
10.00 mL
10.00 mL
5. Calculated density
1.0013 g/mL
g/mL
g/mL
6. Average density of unknown  
flask on balance

Pour the liquid back into the 100 mL beaker (not the waste beaker). After you pour the unknown liquid back into your 100 mL beaker, do not rinse out the flask.

If any liquid is on the outside of the flask, wipe that off.

 

 

pour unknown back in flask
You are now going to repeat the process for Trial 2 and Trial 3. Just grab it with a paper towel again (1), TARE the balance (2) and weigh it again (3).It's OK for some of the liquid to be in the flask. That will be considered just part of the weight of the container (flask). Record the mass of this container (flask) on line 2 for "Trial 2" on the data sheet.
repeat weighing
 
 
Trail 1
Trail 2
Trail 3
1. Mass of container and unknown
74.228 g
g
g
2. Mass of container
64.215 g
64.245 g
g
3. Mass of unknown
10.013 g
g
g
4. Volume of unknown used
10.00 mL
10.00 mL
10.00 mL
5. Calculated density
1.0013 g/mL
g/mL
g/mL
6. Average density of unknown  

True Value   ______________
Absolute Error   ______________
Percent Error   ______________

Just like you did for Trial 1, measure out another 10.00 mL of your unknown liquid using the 10 mL pipette. Add it to your flask and reweigh the flask. Put that reading in line 2 for Trail 2. Repeat these steps one more time to get the Trail 3 data.

After you calculate the density for all three trials, get the average of all three densities. Round the answer to 4 significant figures. Find out the True Value from you instructor and then you can calculate Absolute Error and Percent Error.

set pipette into beaker

Part B

Part B is an alternative method for determining the density of a liquid. It is based on creating a graph the shows mass versus volume. The red data points are the readings of the mass at certain volumes. In Part A you just divided the mass by the volume to get density. That could be done here, but by increasing the volume by increments of 2.00 mL and then finding the mass, you get a graph of how much mass increase there is for a certain volume increase. That ratio (fraction) is the same thing as density. In other words, a density of 1.212 g/mL can be interpreted as an increase of 1.212 g causes an increase of 1 mL. This same ratio is also the slope of the line that is drawn to best fit the data points.

An advantage of graphing your data is that you can see trends better. The trend we see here is that as volume increase so does the mass. We also see that the increase is "linear" meaning the relationship between mass and volume moves in a straight line. In other words, if volume doubles, the mass doubles. Finding the line that best fits the data is similar to finding the average of the data points used to calculate density. Some programs like Excel can analyze the data points and create a line that represents a better average than if you simply found the average by adding all 5 density values and dividing by 5.

graph mass versus volume

Procedure:

Obtain about 10 mL of the same unknown liquid that you used in Part A. (You may have that much left in your 100 mL beaker). Weigh a dry, clean small beaker or Erlenmeyer Flask. (Since you used the 125 mL Erlenmeyer flask for Part A, you can use it for Part B. Just pour the 10 mL of unknown solution from that last weighing back into the 100 mL beaker. Also, the flask doesn't need to be dry. Like before, any residual solution will be subtracted out with the mass of the flask.)

 

pour unknown back in flask
Also, like before, always weigh the flask when it is empty (residual unknown solution is OK). Write the mass of the empty flask, which was 64.123 g in our example. That goes in Part B data sheet. Put the answer in all rows of the third column labeled "Mass of empty flask".
Total Volume of liquid
Mass of flask plus liquid
Mass of empty flask
Mass of liquid
Density of liquid
2.00 mL
g
64.123 g
g
g/mL
4.00 mL
g
64.123 g
g
g/mL
6.00 mL
g
64.123 g
g
g/mL
8.00 mL
g
64.123 g
g
g/mL
10.00 mL
g
64.123 g
g
g/mL
X - Axis
   
Y-Axis
 
set flask on balance

To add 2.00 mL increments, you need a 2.00 mL pipette. Get the pipette from the same area where you got the 10.00 mL pipette. This pipette is also a "TD" (To Deliver) type of pipette.

Remove the 10.00 mL pipette from the pipette pump by unscrewing the white collar. Attach the 2.00 mL pipette in the same manner as you did the 10.00 mL pipette. Be sure to to hold the pipette by the top end as shown in the image. These smaller pipettes are even more breakable so you want to do this properly. Push the pipette into the collar while twisting the green pipette pump as you push in the pipette.

hold 2mL pipette properly
Again, twist the white collar and pipette pump in opposite directions to tighten the collar. It needs to be snug so no air leaks around the compression fitting. attach 2mL pipette

Before you begin adding 2.00 mL increments to the flask, you need to rinse out the 2.00 mL pipette like you did for the 10.00 mL pipette. The pipette may have distilled water, some other unknown liquid inside of it, or some other contamination. Any of these could change the density of your unknown. So you need to rinse it out 3 times.

Draw the liquid so it is about an inch from the pipette pump (as shown). Then move it to the waste beaker and discard the liquid. Do this 2 more times to be sure it's clean.

 

 

2mL pipette getting rinsed

In the same manner of working with the 10.00 mL pipette, draw up your unknown liquid about an inch above the 2.00mL mark. Push the release-lever to drop down the meniscus to be even with the 2.0 mL mark.

Add the liquid to your pre-weighed flask. Like usual, grab the flask with a paper towel and take it to the balance to weigh it.

Eye level view

The task for Part B is add increments of 2.00 mL of your unknown liquid to the flask. Then weigh it after each time you add 2.00 mL. (Don't add liquid to flask while sitting on balance. A spill could damage the balance). Let's say the first weighing after adding 2.00 mL was 66.156 g. That value, of course, would go in the first row under the "Mass of flask plus liquid". You can now subtract the mass of the empty flask to get mass of of the liquid added. In our example, it would be 2.033 g. Density is g/mL, so divide the grams (2.033 g) by the mL (2.00 mL) to get density (1.0165 g/mL).

Total Volume of liquid
Mass of flask plus liquid
Mass of empty flask
Mass of liquid
Density of liquid
2.00 mL
66.196 g
64.123 g
2.073 g
1.0365 g/mL
4.00 mL
g
64.123 g
g
g/mL
6.00 mL
g
64.123 g
g
g/mL
8.00 mL
g
64.123 g
g
g/mL
10.00 mL
g
64.123 g
g
g/mL
X - Axis
   
Y-Axis
 
flask on balance

Draw up another 2.00 mL in your 2.00 mL pipette. Add it to 2.00 mL that you already put into the flask. Remember to touch the tip to the edge of the flask to remove any drop that might be hanging onto the tip. Reweigh the flask, which should now have a total of 4.00 mL of your unknown liquid. Let's say the second weighing was 68.142 grams. Put that answer in the second row. You can now calculate the total mass of liquid (4.054 g) and the density (4.054g/4.00 mL) which calculates as 1.0135 g/mL.

Total Volume of liquid
Mass of flask plus liquid
Mass of empty flask
Mass of liquid
Density of liquid
2.00 mL
66.196 g
64.123 g
2.073 g
1.0365 g/mL
4.00 mL
68.142 g
64.123 g
4.019 g
1.0048 g/mL
6.00 mL
g
64.123 g
g
g/mL
8.00 mL
g
64.123 g
g
g/mL
10.00 mL
g
64.123 g
g
g/mL
X - Axis
   
Y-Axis
 
Flask and pipette
You will repeatedly draw 2.00 mL samples from your unknown solution. After each time you add the 2.00 mL, you will weigh the flask and enter the mass value in the second column. Do this until you have added a total of 10.00 mL. The below table shows the data and calculations after repeating this process with our example data.
Total Volume of liquid
Mass of flask plus liquid
Mass of empty flask
Mass of liquid
Density of liquid
2.00 mL
66.196 g
64.123 g
2.073 g
1.0365 g/mL
4.00 mL
68.142 g
64.123 g
4.019 g
1.0048 g/mL
6.00 mL
70.247 g
64.123 g
6.124 g
1.0207 g/mL
8.00 mL
72.205 g
64.123 g
8.082 g
1.0103 g/mL
10.00 mL
74.364 g
64.123 g
10.241 g
1.0241 g/mL
X - Axis
   
Y-Axis
 

We could find the average of all of these densities like we did in Part A; however, by having a range of volumes and masses, it lends itself to graphing, which has some advantages. One is graphing reveals trends. Also, because we know that a zero volume of liquid will have zero mass, that gives us another data point in our graph. That increases accuracy. Furthermore, by finding a line that best fits the data points, you can get even a better measurement for density.

Draw in more 2 mL samples
To the right is a graph created by Excel with the data above. The small red diamonds are the data points. The light blue line was put in by Excel when you ask for it to include a "trendline." It also asks if the y-intercept (the point where the line crosses the y-axis) is zero. Answering "yes" is correct because we know that at zero volume (x-value) the mass would also be zero (y-value). The formula for a line is y = b + mx where b is the y-intercept and "m" is the slope. Since the y-intercept is zero, b is zero, so we can drop the "b". The slope (m) is the change of Y (change of mass) divided by the change of X (change in volume). That's the same as density. In other words, the slope of this line is a way to calculate the average density. As you can see the red data points sit below and above the line. The line is adjusted visually to go in between the dots. Excel will apply a set of calculations using the data points to find the best fit line (the trendline) mathematically. The formula shown (y=1.0183x) is the formula for the line having a slope of 1.0183. This is for the line that best fits these points. Since the slope is also our density, it is also the most accurate calculation for the density. If we simply averaged the densities from our table, the value would be 1.0193 g/mL, which gets rounded to 3 significant figures. "Averaging" the data by using the slope of the best-fit line comes up with a value of 1.0183 g/mL. That's even a better value. You will learn about these best-fit line calculations in CHM152. For now you will use your eyes for making the best fit line. Graph for Part B

Below is what the graph looks like in the lab manual. The data above was plotted on that graph with red dots. A blue line was drawn to pass by all dots as close as possible (called best-fit line). Be sure to start line at the origin (0,0).

Selected Points on the Fitted Line:
(In theory any two points lets you find the slope; however, the more spread out they are the more difference the get, and you can get more accuracy). Roll cursor over image to see the two points selected as an example. Notice that it is convenient to pick points where one of the coordinates in right on a line. Here we used x values of 1.0 and 11.0 as accurate values for x.

Point 1: X1 = _______ mL            Y1 = ________ g

Point 1: X2 = _______ mL            Y1 = ________ g

Y2 - Y1    Rise = ________ - ________ = _______ g

X2 - X1    Run = ________ - ________ = _______ mL

Slope = Rise / Run = ________ g/mL

Using the data points from our example, the below data is filled in.

Point 1: X1 = 1.0 mL            Y1 = 1.1 g

Point 1: X2 = 11.0 mL            Y2 = 11.3 g

Y2 - Y1    Rise =11.3 g - 1.1 g = 10.2 g

X2 - X1    Run = 11.0 mL - 1.0 mL = 10.0 mL

Slope = Rise / Run =1.02 g/mL

Since our rise and run values had 3 significant figures, we are justified in leaving the answer in 3 significant figures.

PROBLEMS
(Answers must have the correct number of significant figures and the correct units! You must show your method of solution!)
Problems from Lab Manual
Practice Problems and comments
1. If 20.00 mL of a liquid weighs 22.104 g, what is the density? Note that the mL has 4 significant figures and the gram value is 5 significant figures. Your answer is only as accurate the the least accurate measurement used. So the answer should have only 4 significant figures.
2. What is the weight in grams of 30.0 mL of a liquid of density 0.932 g/mL? Practice for 2. What is the weight in grams of 55.0 mL of a liquid that has a density of 1.033 g/mL? The question is asking for grams but we are given mL and density. Use dimensional analysis (factor-label method) to guide you. A table (spreadsheet format) is used to set up the calculation. Notice that the milliliters (mL) cancel out and only grams (g) remain. The 55.0 x 1.033 equals 56.813, but we only have 3 significant figures in "55.0 mL" so our answer is restricted to only 3 significant figures (56.8 g).
 
A
B
C
D
E
F
G
1
Volume of liquid
multiply by density
 
mass (g)
2
55.0
mL
1.033
g
=
56.8
g
3
   
mL      
You could write the above calculations like this:
55.0 mL x 1.033 g = 56.8 g
             mL
3. How many mL of a liquid that has a density of 1.28 g/mL are needed to obtain 40.0 g of the liquid? Practice for 3: The average density of seawater is 1.025 g/mL. If a bucket of seawater weighed 8,345 g and the empty bucket was 322 g, how many mL of seawater is in the bucket? Subtracting the bucket weight, the seawater is 8,023 g ( 8,345g-322g). The answer wanted is in mL and we are given mass (g) and density (g/mL). In our calculation we must cancel grams (g) and get the mL out of the denominator. We need to invert the density to do that. Check out the setup below:
 
A
B
C
D
E
F
G
1
Mass of seawater
density inverted
 
volume (mL)
2
8023
g
1
mL
=
7827
mL
3
   
1.025
g      
Notice that grams cancel and mL is in the numerator. We only had to invert the density values to accomplish that. (Note: It doesn't matter if the density was written in columns A and B and the mass of seawater was in columns C and D) We are justified to have 4 significant figures because both of the starting measurements have 4 significant figures. Problem 3 is similar.
4. How many grams of NH3 are contained in 50.0 mL of a solution that is 22.0% by weight NH3 and has a density of 0.916 g/mL? Practice for 4. The strongest solution of ammonia in water is 35% w/w, and it has a density of 0.87 g/mL. How many grams would one gallon of this solution weigh? The "35% w/w" means there are 35 grams ammonia (NH3) in every 100 grams of solution. Also, 1 gallon = 3,785 mL. The answer is in grams, so we write it at the end. Below is the setup. Everything in red cancels out. What we are left with is just grams of pure NH3. In this case the density was not inverted in order to cancel the mL in D2 and to cancel the "g of solution" in F3.
 
A
B
C
D
E
F
G
H
I
J
K
1
convert gal > mL
concentration of NH3
density of solution
 
g of pure NH3
2
1
gal
3785
mL
35
g pure NH3
0.87
g of solution
=
1152.5
g NH3
3
   
1
gal
100
g of solution
1
mL      

The answer of 1152.5 grams needs to be rounded to 2 significant figures because the concentration and density are both 2 significant figures. So the correct answer is 1200 g NH3 or 1.2x102 g NH3
5. How many mL of concentrated HCl solution are needed to provide 90.0 g of HCl? Concentrated HCl is 37.0% HCl by weight and has a density of 1.19 g/mL. Practice for 5. Concentrated nitric acid is 70.0% nitric acid by weight (70% w/w). Elsewhere on this bottle it says the specific gravity is 1.4 meaning 1.4 g/mL. We need 2,358 grams of pure nitric acid (HNO3). The label says "2.5 L." Is that enough? To answer the question we need to know how many liters of solution is needed to give us 2,358 g of pure HNO3. The answer is in liters but we are given density in g/mL and concentration in grams nitric acid per grams of solution. In "g/mL" the mL is in the denominator. We need "mL" to be in the numerator so that we can have our answer in liters (L).  So the density of 1.4 g/mL will need to be inverted (columns C & D). We also have to invert the concentration (columns E & F) because the answer is liters of the nitric acid solution not of pure nitric acid.
 
A
B
C
D
E
F
G
H
I
J
1
mass of pure HNO3 needed
density inverted
concentration of HNO3 inverted
cancel
milli (m)
 
liters of solution needed
2
2358
g pure HNO3
1
mL
100
g of solution
0.001
=
2.406
L of solution
3
   
1.4
g
70
g pure HNO3
m
     
Notice to cancel the "m" in "mL" so that we are left with just liters, we multiply by 0.001 over "m" because milli is the same as 0.001.  Our answer of 2.406 liters of the concentrated solution will give us the 2,358 grams of pure HNO3.  So our answer is yes, the 2.5 liter bottle is big enough.   Notice the density was only given with 2 significant figures, so our answer of 2.406 L should be reported as 2.4 L. With this practice do Problem 5.